Sylow-metacyclic groups andQ-admissibility |
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Authors: | David Chillag Jack Sonn |
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Institution: | (1) Department of Mathematics, Technion — Israel Institute of Technology, Haifa, Israel |
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Abstract: | A finite groupG isQ-admissible if there exists a division algebra finite dimensional and central overQ which is a crossed product forG. AQ-admissible group is necessarily Sylow-metacyclic (all its Sylow subgroups are metacyclic). By means of an investigation into the structure of Sylow-metacyclic groups, the inverse problem (is every Sylow-metacyclic groupQ-admissible?) is essentially reduced to groups of order 2 a 3 b and to a list of known “almost simple” groups. |
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